We study the Hausdorff Voronoi diagram of a set S of polygonal objects in the plane, a generalization of Voronoi diagrams based on the maximum distance of a point from a polygon, and show that it is equivalent to the Voronoi diagram of S under the Hausdorff distance function. We investigate the structural and combinatorial properties of the Hausdorff Voronoi diagram and give a divide and conque...

bstract. We integrate stylized rendering with an efficient multiesolution image representation, enabling a user to control how ompression affects the aesthetic appearance of an image. We dopt a point-based rendering approach to progressive image transission and compression. We use a novel, adaptive farthest point ampling algorithm to represent the image at progressive levels of etail, balancing...

The MIR Voronoi diagram appears with the notion of good illumination introduced in [3, 4]. This illumination concept generalizes well-covering [7] and triangle guarding [9]. The MIR Voronoi diagram merges the notions of proximity and convex dependency. Given a set S of planar light sources, for each point q in the plane we search for the subset Sq ⊂ S nearest to q and such that q is an interior...

We present a systematic study of the expected complexity of the intersection of geometric objects. We first study the expected size of the intersection between a random Voronoi diagram and a generic geometric object that consists of a finite collection of line segments in the plane. Using this result, we explore the intersection complexity of a random Voronoi diagram with the following target o...

Consider a pair of plane straight-line graphs whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n logn)-time O(n)-space technique to preprocess such a pair of graphs, that enables efficient searches among the red-blue intersections along edges of one of the graphs. Our technique has a number of applications to geometric problems...

The Hausdorff Voronoi diagram of a set of clusters of points in the plane is a generalization of the classic Voronoi diagram, where distance between a point t and a cluster P is measured as the maximum distance, or equivalently the Hausdorff distance between t and P . The size of the diagram for non-crossing clusters is O(n ), where n is the total number of points in all clusters. In this paper...

Power diagrams [Aur87] are a useful generalization of Voronoi diagrams in which the sites defining the diagram are not points but balls. They derive their name from the fact that the distance used in their definition is not the standard Euclidean distance, but instead the classical notion of the power of a point with respect to a ball [Cox61]. The advantage of the power distance is that the ‘bi...

G. Leibon and D. Letscher showed that for general and sufficiently dense point set its Delaunay triangulation and Voronoi diagram in Riemannian manifold exist. They also proposed an algorithm to construct them for a given set. In this paper we estimate the necessary number of points for computing the Voronoi diagram in the manifold by using sectional curvature of the manifold. Moreover, we show...

Voronoi diagram on the earth surface is a powerful tool to study spatial proximity at continental or global scale. However, its computation remains challenging because geospatial features have complex shapes. This paper presents a raster-based algorithm to generate Voronoi diagrams on earth's surface. The algorithm approximates the exact point-to-point geographical distances using the cell-to-c...

In this paper we describe a new method of position detection for a mesh-backed printing screen with an alignment mark that is overlapped by mesh patterns. A circular hole is selected as an alignment mark so that at least a portion of its contour can be observed through the windows of the mesh wires. To recognize the true contour, the smallest circle enclosing binary patterns acquired with a tra...